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Hurt? Nope. At worst it won't taste as good or have the same texture as it otherwise would, but who knows you may like it better.

I always like to eat the veggies from the stock or soup since a kid and I'm still alive (I think) and I don't strain it because when I place in fridge overnight the crap marry's and it tastes even better the next day.

I'm with simon. There is no way they could hurt you. They could harm your sensibilities, but they won't hurt you physically.

Where are the realchiffonade and Hungryinhouston when you need them? We had a thread not too long ago about your favorite cook's treat; they eat everything from the veggies to the bones. Of course, they might be crazy. shhh...
Really though. If you can eat the stock, you can eat what's in it without harm.

I've never heard of anyone actually strainging anything out of chicken soup. I'm curious why you would want to? I mean aside from straining the bones out before adding the vegetables to make the soup.

They'll be like mush but they won't hurt you. That's a great cook's treat! (And you can gnaw on the neck, too.)

I like my chicken soup clean. I don't think there is anything harmful, just unappetizing. Once I've discarded everything that has given it's life and flavour, I then start adding soup vegetables and meat. If I'm going to use noodles, I cook and keep them separate, and add to hot soup when serving, to prevent overcooked pasta (yuk). I've been sick and all I really want is soup, and lots of it. I never seem to tire of it.

Slightly off topic, but if you use vegetables as a rack for large cuts of meat like pot roast, turkey, etc., you can mash those veggies (or puree in the food processor) and add them back into the gravy. You can do the same for some types of soups, too.

@Perkymac never thought to puree the crap and throw into gravy, that sounds good, have to try it next time I make it, thanks.

...sucked up all the "dirty" stuff of the chicken...

Not sure what exactly you're referring to... dirty stuff??? Could you elaborate?

As far as eating the veggies, meat, etc... if you like it, eat it. Personally, I find it completely flavorless, and the texture is... well... blech. But, personal preferences aside, it's all food... You'd eat it if were cooked any other way, right? Why would turning it into stock suddenly make it harmful?

Regarding clarity, foam, cloudiness, etc., if you are careful to never allow your stock to reach a boil, and resist the urge to stir it, then it shouldn't get very cloudy. Keep it at no more than barely simmering and keep your hands off. More often than not, you also won't have any foam if you follow this technique. If you do get some foam, and it bothers you, carefully skim it off the surface, but do not stir.

If you don't want to eat them, the best way to remove the solids without clouding up your stock is to carefully scoop out as much of the liquid as possible with a ladle. Avoid stirring up the solids and do not press down on them to get at the broth. Once the bulk of the liquid is out, carefully scoop out the larger solids, ladle out more stock and, finally, dump the rest of the pot into a regular mesh kitchen sieve over a bowl. If I'm using my stock for a brothy soup, I usually don't add this small amount of cloudier stock, just because it's not that attractive. I save it for things like gravy or bean soups. But I never go so far as to use cheesecloth, because I'm only concerned with the flavor, not how it looks. I never bother to clarify the stock for the same reasons.

Like I said above I love those veggies and I would hire guards to watch over them, yes they are mushy and have aborbed all the yummies they have been simmering all this time and boy do they taste good, I may add a new batch of veggies but the old ones are for me.